For each positive integer

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For each positive integer nn, consider the point PP with abscissa nn on the curve y2−x2=1y^2 - x^2 = 1. If dnd_n represents the shortest distance from the point PP to the line y=xy = x, then lim⁡n→∞(n⋅dn)\lim_{n \to \infty} (n \cdot d_n) has the value equal to (1) \frac{1}{2\sqrt{2}} (2) \frac{1}{2} (3) \frac{1}{\sqrt{2}} (4) 0

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